Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Dec 1410:00 AM EST
-12:00 PM EST
Think a 100% GMAT Verbal score is out of your reach? Target Test Prep will make you think again! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
Dec 1411:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.
Dec 1310:00 AM EST
-12:00 PM EST
Have you ever wondered how to score a PERFECT 805 on the GMAT? Meet Julia, a banking professional who used the Target Test Prep course to achieve this incredible feat. Julia's story is nothing short of an inspiration.- Dec 15
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Dec 1608:00 AM PST
-11:59 PM PST
GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes!- Dec 17
09:00 AM PST
-10:00 AM PST
Join Manhattan Prep instructor Whitney Garner for a fun—and thorough—review of logic-based (non-math) problems, with a particular emphasis on Data Sufficiency and Two-Parts. - Dec 18
10:00 AM PST
-11:00 AM PST
Here is the essential guide to securing scholarships as an MBA student! In this video, we explore the various types of scholarships available, including need-based and merit-based options.
29 Jun 2011, 09:38
Kudos
Bookmarks
Bunuel
Lately, many questions were asked about the standard deviation. So I'm posting here my collection of DS problems on SD, plus some tips about it.
Please note the following:
A. I was assured MANY TIMS, by various GMAT tutors, that GMAT won't ask you to actually calculate SD, but rather to understand the concept of it. Though KNOWING how it's calculated helps in understanding the concept.
B. During the real GMAT it's highly unlikely to get more than one ot two question on SD (as on combinatorics), actually you may see none, so do not spend too much of your preparation time on it, it's better to concentrate on issues you'll definitely face on G-day.
Many questions below are easy, some are tough, but anyway they are good to master in solving SD problems. I'll post OA after some discussions. Please provide your way of thinking along with the answer. Thanks.
Here we go:
1. What is the standard deviation of Company R’s earnings per month for this year?
(1) The standard deviation of Company R’s earnings per month in the first half of this year was $2.3 million.
(2) The standard deviation of Company R’s earnings per month in the second half of this year was $3.9 million.
2. What is the standard deviation of Q, a set of consecutive integers?
(1) Q has 21 members.
(2) The median value of set Q is 20.
3. Lifetime of all the batteries produced by certain companies have a distribution which is symmetric about mean m. If the distribution has a standard deviation of d , what percentage of distribution is greater than m+d?
(1) 68 % of the distribution in the interval from m-d to m+d, inclusive
(2) 16% of the distribution is less than m-d
4. Question deleted
5. List S and list T each contain 5 positive integers, and for each list the average of the integers in the list is 40. If the integers 30,40 and 50 are in both lists , is the standard deviation of the integers in list S greater than the standard deviation of the integers in list T?
(1)The integer 25 is in list S
(2)The integer 45 is in list T
6. Set T consists of odd integers divisible by 5. Is standard deviation of T positive?
(1) All members of T are positive
(2) T consists of only one member
7. Set X consists of 8 integers. Is the standard deviation of set X equal to zero?
(1) The range of set X is equal to 3
(2) The mean of set X is equal to 5
8. {x,y,z}
If the first term in the data set above is 3, what is the third term?
(1) The range of this data set is 0.
(2) The standard deviation of this data set is 0.
9. Question deleted
10. A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?
(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.
11. During an experiment, some water was removed from each of the 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?
(1) For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:
1. Find the mean, m, of the values.
2. For each value xi calculate its deviation (xi-m) from the mean.
3. Calculate the squares of these deviations.
4. Find the mean of the squared deviations. This quantity is the variance.
5. Take the square root of the variance. The quantity is th SD.
TIPS:
1. |Median-Mean| <= SD.
2. Variance is the square of the standard deviation.
3. If Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.
4. SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).
5. Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.
6. If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.
7. If we increase or decrease each term in a set by the same percent:
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
8. Changing the signs of the element of a set (multiplying by -1) has no effect on SD.
9. The SD of any list is not dependent on the average, but on the deviation of the numbers from the average. So just by knowing that two lists having different averages doesn't say anything about their standard deviation - different averages can have the same SD.
You can also check collection of PS questions of SD at: ps-questions-about-standard-deviation-85897.html
Please note the following:
A. I was assured MANY TIMS, by various GMAT tutors, that GMAT won't ask you to actually calculate SD, but rather to understand the concept of it. Though KNOWING how it's calculated helps in understanding the concept.
B. During the real GMAT it's highly unlikely to get more than one ot two question on SD (as on combinatorics), actually you may see none, so do not spend too much of your preparation time on it, it's better to concentrate on issues you'll definitely face on G-day.
Many questions below are easy, some are tough, but anyway they are good to master in solving SD problems. I'll post OA after some discussions. Please provide your way of thinking along with the answer. Thanks.
Here we go:
1. What is the standard deviation of Company R’s earnings per month for this year?
(1) The standard deviation of Company R’s earnings per month in the first half of this year was $2.3 million.
(2) The standard deviation of Company R’s earnings per month in the second half of this year was $3.9 million.
2. What is the standard deviation of Q, a set of consecutive integers?
(1) Q has 21 members.
(2) The median value of set Q is 20.
3. Lifetime of all the batteries produced by certain companies have a distribution which is symmetric about mean m. If the distribution has a standard deviation of d , what percentage of distribution is greater than m+d?
(1) 68 % of the distribution in the interval from m-d to m+d, inclusive
(2) 16% of the distribution is less than m-d
4. Question deleted
5. List S and list T each contain 5 positive integers, and for each list the average of the integers in the list is 40. If the integers 30,40 and 50 are in both lists , is the standard deviation of the integers in list S greater than the standard deviation of the integers in list T?
(1)The integer 25 is in list S
(2)The integer 45 is in list T
6. Set T consists of odd integers divisible by 5. Is standard deviation of T positive?
(1) All members of T are positive
(2) T consists of only one member
7. Set X consists of 8 integers. Is the standard deviation of set X equal to zero?
(1) The range of set X is equal to 3
(2) The mean of set X is equal to 5
8. {x,y,z}
If the first term in the data set above is 3, what is the third term?
(1) The range of this data set is 0.
(2) The standard deviation of this data set is 0.
9. Question deleted
10. A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?
(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.
11. During an experiment, some water was removed from each of the 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?
(1) For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:
1. Find the mean, m, of the values.
2. For each value xi calculate its deviation (xi-m) from the mean.
3. Calculate the squares of these deviations.
4. Find the mean of the squared deviations. This quantity is the variance.
5. Take the square root of the variance. The quantity is th SD.
TIPS:
1. |Median-Mean| <= SD.
2. Variance is the square of the standard deviation.
3. If Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.
4. SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).
5. Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.
6. If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.
7. If we increase or decrease each term in a set by the same percent:
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
8. Changing the signs of the element of a set (multiplying by -1) has no effect on SD.
9. The SD of any list is not dependent on the average, but on the deviation of the numbers from the average. So just by knowing that two lists having different averages doesn't say anything about their standard deviation - different averages can have the same SD.
You can also check collection of PS questions of SD at: ps-questions-about-standard-deviation-85897.html
Hi Bunuel,
I find the collection of questions that you posted on Standard Deviation very helpful. Do you post questions like this on all the other topic as well?
01 Jul 2011, 16:00
Kudos
Bookmarks
Great collection of excellent questions...
saurabhkhatrinitk
Joined: 29 Jan 2012
Last visit: 08 Jan 2019
Posts: 6
Own Kudos:
Given Kudos: 5
Schools: Darden '15 (S)
18 Mar 2012, 11:43
Kudos
Bookmarks
[quote="Bullet"]I'll try to provide some explanation of the questions with reference to answers, please correct me if i'm wrong.
Thanks
ANSWERS (OA):
1. What is the standard deviation of Company R’s earnings per month for this year?
(1) The standard deviation of Company R’s earnings per month in the first half of this year was $2.3 million.
(2) The standard deviation of Company R’s earnings per month in the second half of this year was $3.9 million.
Answer: E.
Reason : As none of the information above is adequate to find the SD, therefore SD is not possible to calculate
Wanted to make a point here, please clarify if im wrong that SD is calculated as follows:
standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(m-x_i)^2}{N}}.
and the two statements give me the values inside the function hence can be used to calculate the SD for the entire year...
Thanks
ANSWERS (OA):
1. What is the standard deviation of Company R’s earnings per month for this year?
(1) The standard deviation of Company R’s earnings per month in the first half of this year was $2.3 million.
(2) The standard deviation of Company R’s earnings per month in the second half of this year was $3.9 million.
Answer: E.
Reason : As none of the information above is adequate to find the SD, therefore SD is not possible to calculate
Wanted to make a point here, please clarify if im wrong that SD is calculated as follows:
standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(m-x_i)^2}{N}}.
and the two statements give me the values inside the function hence can be used to calculate the SD for the entire year...
